Linear Equation

Define Linear, Quadratic and Simultaneous Equations

A linear equation has variables with no exponent higher than 1. A quadratic equation contains at least one variable squared. Simultaneous equations are a set of multiple equations that share the same unknown variables, which are solved together to find matching values for those variables. [1, 2, 3, 4]

Here is a quick breakdown of each concept:

1. Linear Equations

A linear equation represents a straight line when graphed. The highest power of any variable in the equation is always 1.

Standard Form: $ax + by = c$ (where $a$, $b$, and $c$ are numbers, and $x$ and $y$ are variables)
Example: $3x + 4 = 10$ [6, 7]

2. Quadratic Equations

A quadratic equation is a second-degree polynomial, meaning the highest power of the unknown variable is exactly 2. When graphed, they form a U-shaped curve called a parabola.

Standard Form: $ax^2 + bx + c = 0$
Example: $x^2 - 5x + 6 = 0$
Note: These can be solved using factoring, completing the square, or the quadratic formula$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ [1, 2]

3. Simultaneous Equations

Simultaneous equations (or systems of equations) require you to find values for two or more unknown variables that make all the equations true at the same time. Graphically, the solution represents the exact point or points where the lines or curves cross each other.

Example (System of Linear Equations):$x + y = 5$$2x - y = 4$
Note: Simultaneous equations can also be a mix, such as a linear and quadratic system. You can solve these using methods like substitution (plugging one equation into the other) or elimination (adding/subtracting equations to cancel out a variable). [2, 3, 11, 12, 13]